What are examples of optimization problems that can be solved using genetic algorithms?
There are numerous problems that can be solved with genetic algorithms or, more generally, with evolutionary algorithms (which includes also genetic programming and evolutionary strategies), even though they may not necessarily be the most efficient approach.
Here are a few examples.

Evolution of the topology of neural networks. This is called neuroevolution.
Automatic test case generation (in particular, for self-driving cars). AsFault is one specific example.
Design of novel quantum computing algorithms. Specifically, genetic programming has been used to solve this problem (see this reference for more details).
As an alternative to reinforcement learning algorithms to solve RL problems. Specifically, evolution strategies have been successfully used in this case (see this).

There is a Wikipedia article that lists many other applications of genetic algorithms: List of genetic algorithm applications.